It is generally desirable that a grinding wheel should be in a condition of relatively good balance in order to give satisfactory results when used in a grinding operation and also to reduce the loading on the grinding wheel mounting arrangement. One form of apparatus for unbalance compensation of a grinding wheel rotatable about an axis of rotation, as disclosed in EP 0 409 050 A2, comprises two compensating weights which are guided rotatably about the axis of rotation with symmetrical mass distribution relative to a central plane of the grinding wheel, which is perpendicular to its axis of rotation. The two compensating weights are adjustable about the axis of rotation of the grinding wheel on equal radii at different angular Positions to provide for grinding wheel unbalance compensation. The apparatus includes positioning means for setting the compensating weights at different angular positions. When positioning the compensating weights at different positions, the centers of gravity of the compensating weights move in the central plane of the grinding wheel and thus the compensating weights afford symmetrical distribution of mass relative to the central plane of the grinding wheel, which is perpendicular to the axis of rotation thereof. That configuration provides a moment-free balancing system in comparison with grinding wheel balancing systems in which the centers of gravity of the compensating weights move in different planes. It is for that purpose that the compensating weights which are in the form of segments of a hollow cylinder and more specifically shell portions constituted by quarters of a cylinder, are moved on the same radius around the above-mentioned axis of rotation.